A Holomorphic Operator Function Approach for the Laplace Eigenvalue Problem Using Discontinuous Galerkin Method
Year: 2021
Author: Yingxia Xi, Xia Ji
CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 4 : pp. 776–792
Abstract
The paper presents a holomorphic operator function approach for the Laplace eigenvalue problem using the discontinuous Galerkin method. We rewrite the problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence for the discontinuous Galerkin method is proved by using the abstract approximation theory for holomorphic operator functions. We employ the spectral indicator method to compute the eigenvalues. Extensive numerical examples are presented to validate the theory.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2021-0012
CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 4 : pp. 776–792
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Discontinuous Galerkin method eigenvalue problem Fredholm operator.